"Modeling single crawling cells with a phase field approach"; Dr. Benjamin Winkler (University of Freiburg)

Aug 05
05-08-2019 16:00 Uhr bis 17:00 Uhr
Übung 1, 01.250-128

ABTSRACT: Motile single cells play major roles in the viability of higher organisms. For instance, they are
involved in morphogenesis, wound healing, the immune response and in pathologies such as metastasis
in late-stage cancer. For a physicist, biological cells are highly complex systems far from equilibrium
that actively generate forces on a molecular scale in order to adapt their shape or even move in response
to external stimuli. The many orders of magnitude involved and the complex biochemical regulatory
pathways present tough challenges for potential modeling approaches. One route to model whole cells
lies therefore in coarse-graining the molecular details to arrive at a continuum description via partial
differential equations. As a numerical scheme, the phase field approach allows for the efficient tracing
of the cell membrane due to the introduction of a continuous, auxiliary field. By coupling additional
dynamical fields, it becomes possible to model specific aspects of cell motility – such as adhesion,
substrate deformability, collective dynamics or the role of membrane tension – in a modular manner.
The model was introduced as an effective 2D description for cells crawling on flat substrates by
means of a flat, fanlike protein structure called the lamellipodium [1]. In vivo, however, cells experience
a much more diverse environment with heterogeneous adhesive and mechanical properties, as well as
various substrate geometries confining the cell body and presenting purely geometric guiding cues for
the cell’s motility apparatus. With our recent generalization of the model to 3D, we were able to
address cell motility in practically arbitrarily shaped environments [2]. By systematically studying the
effects of vertical confinement, substrate curvature and surface topography we examined the major
in vitro model scenarios for 3D cell migration that are increasingly realized in experiments. Without
including specific biochemical regulatory pathways, our minimalist model reveals several aspects of how
substrate geometry controls cell migration in complex environments.